7
advanced-math

A substance has 90% remaining after 10 minutes. What is the decay function if starting with 500 grams?

A

A(t)=500(0.9)t/10A(t) = 500(0.9)^{t/10}

B

A(t)=500(0.1)t/10A(t) = 500(0.1)^{t/10}

C

A(t)=500(0.9)10tA(t) = 500(0.9)^{10t}

D

A(t)=450(0.9)tA(t) = 450(0.9)^t

Correct Answer: A

Choice A is the correct answer. Model the decay pattern.

  1. Retention: 90% remains means factor b=0.9b = 0.9.
  2. Time Period: Every 10 minutes, so exponent is t10\frac{t}{10}.
  3. Equation: A(t)=500(0.9)t/10A(t) = 500(0.9)^{t/10}.
  4. Verify: At t=10t=10, A=500(0.9)1=450A = 500(0.9)^1 = 450 (90% of 500) ✓

💡 Strategic Tip: 90% remaining = factor of 0.9, not 0.1.

Choice B is incorrect because 0.1 would mean only 10% remains. Choice C is incorrect because exponent should be t/10t/10, not 10t10t. Choice D is incorrect because initial value is 500, and decay happens per 10 min.